In PET, a positron-emitting substance is injected into a human or animal body or into another object to be monitored. The substance, which is usually also referred to as radio pharmaceutical or radiotracer, is selected such that it is adsorbed in certain regions of the object, e.g. in regions which are of interest for the diagnosis of certain diseases. For instance, the substance may be adsorbed by tumor cells so that such cells can be detected in PET images of a human or animal body.
When a positron is emitted by the radiotracer, an encounter with a nearby electron annihilates the electron positron pair and produces a pair of annihilation photons. Each of these annihilation photons has an energy of 511 keV and both photons travel in substantially opposite directions. These photons are recorded by the PET detector substantially at the same time as a so-called coincidence. From such coincidences, PET systems reconstruct a so-called activity distribution or activity map, which shows the spatial distribution of the electron positron annihilation rate within the object. The activity distribution substantially corresponds to the spatial distribution of the radiotracer within the object, which can thus be evaluated for diagnostic or other purposes.
Usually, the activity distribution is determined on the basis of true coincidences, i.e. coincidences comprising two annihilation photons that travel unimpeded to the PET detector and hit the detector at opposing locations with their original energy of 511 keV. However, it is not possible to reconstruct the activity map based on the true coincidences alone, because not all annihilation photons reach the detector unimpeded due to photon attenuation. Attenuation particularly occurs when a photon is absorbed before it reaches the detector or when it undergoes inelastic Compton scattering one or more times (where a scattered photon may reach the detector but has a lower energy). In order to take account of these effects, attenuation correction has to be performed when determining the activity map. Without such attenuation correction, regions having a high activity and a high attenuation probability for photons originating from this region would appear as regions with a smaller activity.
Attenuation correction requires the knowledge of a so-called attenuation map or attenuation distribution, which provides the spatial distribution of the photon attenuation rate. In combined PET and Computed Tomography (CT) imaging system, such an attenuation map is readily available. So, the CT images correspond to attenuation maps for X-ray photons and can be up-scaled to the energy of the annihilation photons. Also for standalone PET systems and systems combining PET with a different imaging modality than CT, such as for example Magnetic Resonance Imaging (MRI), techniques for determining the attenuation map have been developed. One approach, which is also referred to as Maximum-Likelihood Reconstruction of Attenuation and Activity (MLAA) is particularly described in the publication J. Nuyts et al., “Simultaneous maximum a posteriori reconstruction and activity distribution from emission sinograms”, IEEE Trans. Med. Imaging 18 (1999), 393-403. In this approach, both the activity distribution and the attenuation map are reconstructed from PET measurement data. However, this approach does usually only allow to determine relatively rough estimates of the attenuation map.
A further technique for determining the attenuation map is described in the publication Y. Berker, F. Kiessling and V. Schulz, “Scattered PET data for attenuation-map reconstruction in PET/MRI”, Med. Phys. 41 (10), October 2014, 102502. In accordance with this technique, an estimate of the attenuation map is reconstructed on the basis of single-scattered coincidences. These coincidences respectively include one annihilation photon reaching the PET detector unimpeded and one annihilation photon that is scattered a single time. In order to determine the attenuation map, the single-scattered coincidences are calculated by means of a model calculation on the basis of an estimate of the attenuation map, and the calculated single-scattered coincidences are compared with the measured single-scattered coincidences. On the basis of this comparison an attenuation map minimizing the difference between the calculated and measured single scattered coincidences is determined. For this purpose an iterative procedure is applied.
This technique allows for a relatively precise estimate of the attenuation map. However, the technique involves a high computational complexity. So, the calculation of single-scattered coincidences is a numerical calculation performed on the basis of a grid that divides the detector volume into grid elements, which are usually also referred to as voxels. For the calculation of the single-scattered coincidences, one attenuation value from the estimate of the attenuation map is assigned to each voxel. This leads to a large number of required calculation steps, which makes the technique relatively slow and impedes its use in practical applications.